Alex Kasman(click on names to see more mathematical fiction
by the same author)

Highly Rated!

Note: This work of mathematical fiction is recommended by Alex for young adults and math majors, math grad students (and maybe even math professors).

The stories in this collection of 16 original short works of mathematical fiction are different from each other in many ways: some are serious and some funny, some are realistic and some fantastical, some take place in the future others in the past. What they have in common (aside from the fact that I wrote them) is a connection to mathematics and mathematicians.

It is obviously difficult for me to write impartially about my own book, so I am very grateful to Andrew Breslin, Sonja Dezman and Mark Nelson (see below) for writing in with their reactions to it. I hope that more people, including those with different views, will write in as well. I also encourage you to read the review by John Swallow which appeared in the AMS Notices and is available here.

Contributed by
Sonja Dezman

Kasman's »Reality Conditions« is a wonderful book. It is a good example of what mathematical fiction should be like.
Reality conditions is a set of short stories. Although they are written by the same author each of them is unique. The only thing that they have in common is mathematics. There are 16 stories. Some of them are longer, some of them are shorter. You can read the stories separately or you can read them together, at the same time, as a whole. The main characters are all connected to mathematics. There are mathematicians, math professors, math students, children, grandparents, ordinary people, etc. What surprised me most is that, often, the main characters are women. If Alex Kasman was a women I would say that he is a feminist writer and his stories are feminist stories. But he is a man!!! Can a man be a feminist writer? It is a huge puzzle to me why Kasman decided to give women such a big role in his stories. I am a bit sceptical about male authors putting female characters in their stories. I don’t think that any man knows what is it like to be a woman mathematician. In fact, to tell you the truth, I never knew that the character I was reading about is female until I saw “her”, “she” and other indicators of a female person . I respect Kasman for using female mathematicians and I think that it is a brilliant idea to put women more “power”. Now that I think of it, I love Kasman’s book mostly because he used women mathematicians so often. It is just that the book is not womanish enough (according to the amount of women characters).

Well, it doesn’t really matter whether the book is womanish enough or not. The book is a collection of mathematical fictional stories. That means that we (I) should focus on the mathematics that it uses. These stories cover different areas of mathematics. There are topology, geometry, the number theory, and many more. We read about theorems, proofs, mathematicians, Egyptian mathematics, the use of maths in every day life, etc. Some stories are written in the past, some in the present and some in the future. The settings are different. Even different genres are used. There are crime stories, adventures, science fictional stories, legends, and so on. There are murders and love stories, families and individuals, people and aliens, students and professors, ordinary people and mathematicians. All these parts are like little pieces of a big puzzle. They are of different colour, different size, different shape, and different dimension. Putting the pieces together according to their size, shape, colour, or dimension is easy, but that doesn’t make the puzzle complete. Alex kasman found a way to put the right pieces together to make the puzzle perfect and complete. That makes him an excellent writer!
I haven’t written a lot about mathematics. That is because I’d like to get into these stories more deeply, read them again and think more about them. I’ll tell you more about each story, particularly about the mathematics that it uses. It is impossible to talk about it in general, because each story is so unique and precious. It would be a crime to generalize things at this stage.

All I can say for now is that I was absolutely impressed by the way that mathematics is used. The stories are often ironic. And they achieve that ironic tone by using mathematics. Through the use of mathematics Kasman is reminding us that we are not the smartest beings.

There are some stories that I didn’t understand. To tell you the truth, most of the mathematics that is used is unknown to me (and I’m a math student). But that is not a problem at all. The book could be read by everyone. Mostly the knowledge that we need is explained within the story itself. It is up to us whether we want to know more about it or not. But you definitely don’t need to be a mathematician to understand the messages that are behind these stories.

I hope that by now you have realized that you simply have to read Kasman’s “Reality Conditions”. There are so many different mathematical areas, genres, settings and characters used that I’m certain you’ll find something that you’ll like. Enjoy reading Kasman’s book as much as I did! :-) P.S.: My favourite story is “Pop Quiz”. Which is yours?;-)

Thank you for the kind words, Sonja. I am very pleased that at least one person seems to have enjoyed the book. (BTW, my mom hated it.) Let me just comment briefly on the "feminism" aspect. I really don't think that a woman mathematician need necessarily be very different from me...no more or less so than another male mathematician. Consequently, I did not make any effort to capture the "uniquely feminine" aspects of the characters at all. It was quite intentional on my part that some of the characters are male and some of the characters are female, but the stories could be rewritten with the genders reversed and essentially no other changes. Does that make me a feminist writer? (P.S. My favorite story is "Monster" ;-)

The stories in this collection are:

Unreasonable Effectiveness: A fantasy which proposes a fantastical explanation to the famous question of why abstract mathematics is so useful in the real world. This is the only story in the collection which was previously published. (The rest are brand new.)

Murder, she conjectured: A police psychologist attending a conference in Cambridge, England is pulled into an unsolved murder mystery by her mathematician boyfriend. An important theme of the story is the oppresive sexism that discouraged women from entering the field of mathematics in the 19th century.

The Adventures of Topology Man: The subject of topology is one of the most versatile and least appreciated areas of mathematics. In this parody of comic books, the role of topology is illustrated through the powers of the superhero Topology Man.

Eye of the Beholder: A mathematician battles depression after the death of her husband and child in a car accident, and faces difficult moral decisions when she discovers the methods that the government is using to read encrypted messages. Three major themes in this story are the role of number theory in cryptography, the subjectivity of aesthetics in both art and mathematics, and the possibility that the underlying structure of human thought is itself mathematical.

Reality Conditions: The title story follows a mathematics grad student on his quest to prove an important theorem and make a place for himself in mathematical history. The plot and characters are based on the famous Sumerian myth of Gilgamesh. However, instead of real immortality, the hero is seeking the sort of immortality that mathematicians like Newton and Gauss achieved through their work and instead of gods, he interacts with the leading mathematicians and physicists.

The Exception: An old man recalls his work on an undergraduate research project in which he helped a professor disprove Goldbach's Conjecture.

Pop Quiz: An algebraic geometer is called in when messages from an alien spacecraft appear to be asking questions about projective varieties.

The Math Code: Mathematical notation is utilized as a code, allowing a kidnapped mathematician to communicate with his colleagues.

Monster: In a futuristic world where college courses are supported by advertising, funding of grant research is determined by a popular vote, and advanced mathematics is directly marketed to consumers, a group theorist going through her midlife crisis is caught in a scandal that may destroy her career forever. The story includes a relatively detailed introduction to group theory, with a special emphasis on the famous "Monster Group". Another theme in this (hopefully) humorous and compelling tale is plagiarism in academia.

The Corollary: A mathematician whose career has been strongly influenced by the "Publish or Perish" tenure policy at his university reconsiders his goals.

Maxwell's Equations: This story puts you inside the head of James Clerk Maxwell as he discovers the existence of electro-magnetic waves merely by manipulating formulas.

Another New Math: A mathematician and his young daughter try to convince a school board to consider teaching advanced mathematics to elementary school children.

The Center of the Universe: A student discovers a message, apparently placed there just for him, hidden in the decimal expansion of the number pi.

the object: A mathematician faces the possibility of a horrific and painful death unless she can figure out how to destroy the instanton produced by her invention.

The Legend of Howard Thrush: This is a parody of the American Folk Tale genre (e.g. Paul Bunyan and Pecos Bill) with a mathematical protagonist.

Progress: A young man rediscovers and criticizes the multiplication algorithm used by the ancient Egyptians, and then is forced to reconsider his views when he later encounters the algorithm again in a very modern context.

Contributed by
Alex Kasman

(January 4, 2006)
Well, I've read my first official review of Reality Conditions (to appear in the Mathematical Intelligencer), and I am happy to report that it wasn't as bad as I feared! It was not a rave review, by any means. However, since I'm a mathematician and not a real author, I feared that the reviews would say that I could not write and that the book should never have been published. Instead, the review by Mary Gray at American University says "What Kasman is very good at is creating the world in which mathematicians work. From the anxious graduate student, to the novice Ph.D., to the disillusioned professor, to the distinguished expert, and from the isolation of a shabby office, to the interchanges at a coffee bar, to the atmosphere at MSRI, mathematicians will recognize themselves, their colleagues, and their surroundings." I really like that because that is really what I was trying to do.

Still, the review in general is far from complimentary. The reviewer's main complaint is that the book will not be interesting to or readable by non-mathematicians. This would be very disappointing to me, since my goal in writing it was to provide a glimpse of the world of mathematics to non-mathematicians. However, I respectfully disagree with Gray. Perhaps the difference in our opinions is in part due to a different idea of who that audience would be. I was imagining the audience to be made up of people with a serious interest in science and math (perhaps undergraduates majoring in science or math, or older folks who always wished they had learned more about these subjects). In contrast, Gray's opening sentences suggest that she is considering the book as an attempt to reach academics in the social sciences and humanities. (She says "Whatever its deficiencies, C. P. Snow’s Two Cultures [1] concept of mutually incomprehensible dialogue between scientists and others lives on. For as intriguing as the collection of short fiction in Reality Conditions might be to mathematicians, it is difficult to believe that many of the stories would appeal to, or indeed be understood by, those on the `other side' of the cultural divide.") In any case, I have some experience to back up my claim that the stories in this book are not inaccessible to my intended audience. I have twice taught a special topics course here at the College called Mathematics in Fiction in which students from all different majors read some of the works of fiction mentioned on this website (including a few from my book). This experience has given me a good understanding of what sorts of fiction can and cannot effectively convey some of the deeper realities of mathematics to non-mathematicians, and I still believe the stories in my book can do so. Still, though it would be a shame, I admit that my opinion here may be biased and Professor Gray might be right. (This is your cue. You...the person reading this right now. Please read the book and write in with your opinions by clicking on the "vote" link below. I'd happily post them here for others to see!)

Just one more comment: Gray's review suggests a lapse into sexism on my part in the story Topology Man when I named the female character Category Theory Girl. I was well aware of the inequity in calling one character "man" and the other "girl", but this was supposed to be a parody of comic books where this sort of sexism is the norm.

I've been thinking for a few years that
a good way to broaden the mathematical horizons of our students would be
to run a "mathematics in fiction" course. Give
them some fiction, find out which stories they liked the most
and then ask them to follow up on the mathematical ideas within the
stories. I don't think I'll ever get a chance to run this course,
but I have been collecting books along the way. Your collection
of short stories is ideal for this purpose.

The August 2006 issue of the Notices of the AMS includes a very positive review of Reality Conditions! You can read it here.

Note Added February 2007: I just learned that Reality Conditions was selected as a "Best Science Book for High School Students 2005" by the A.A.A.S and their "SB&F" program. See here for more information about that. (You know, when I wrote the book I had college students in mind as a potential audience. I'm not sure I would agree that it is appropriate for high school students. I wonder if any high school teachers have experience sharing this book with their students and could write in with their own thoughts on this.)

Contributed by
Andrew Breslin

With the exception of a rapidly shrinking handful of humans and one cat, there is nothing I love in this world more than words and numbers. And of the two, numbers are much better behaved. But most people don't use them very well, and the few who do have a disturbing tendency to use words like blunt and rusty instruments, and hold them the wrong way too. So it was an unexpected delight to stumble upon this marvelous little book. A collection of stories that greatly stimulated my interest in a wide range of mathematical topics, some familiar, some esoteric, but every one of them expressed in the context of a damn good story. Who could ever have anticipated that? Seriously, I've had a few math teachers in my time who were utterly incapable of assembling a coherent sentence and just hurled a fusillade of words at the class in the vain hopes that they would spontaneously assemble themselves into phrases and clauses. They would become hopelessly enmeshed in their tangled web of words and numbers, as the class would wriggle helplessly and elucidation flitted away, never to be seen again. And yet here is one who not only knows how to use words, but to actually spin a yarn.

I dabble with mathematical fiction myself, but when I ran the premise of my second (math-heavy) novel by the publisher of my first, she could hardly contain her lack of enthusiasm. "People who read fiction don't like math," she opined. "People who like math don't read fiction." She then made a little Venn diagram, just to make sure her point was not lost upon me, what with the imprecise tools, words, with which she customarily expresses herself. It showed the intersection of the two sets to contain a single element, me. I now know that there is at least one other element in that set! It is not a singleton set! Woohoo!

Kasman has proven to be nearly as skilled with words as he is with numbers. Or so I suspect, as his mathematical expertise is so far beyond my own that not only do I not really understand it, I can not even make pithy jokes about it, and I have thus far found very little about which I will not try to crack wise. Sumerian funereal rites, amoebic dysentery, Cantorian set theory, hell there's just a treasure trove of potential risible brilliance here. But even if I could find something humorous about permanent localized disturbances in non-linear waves, or Grassmannian manifolds and associated functions which satisfy nonlinear partial differential equations, nobody would get it.

(Aside: I am hereby offering a prize to anyone out there who can make a funny joke on the above subjects and explain it to me. Extra credit will be given for an explanation incorporating cusp catastrophe models. The preceding item is not a joke.)

I confess to a certain sadistic delight in crafting humor that 99% of people will not get. Some of my fellow arrogant jackasses are with me on this. Because you know that the 1% who do get it will really appreciate it. Also, you can immediately lower your opinion of everyone who doesn't laugh. So really: what's not to love about Kasman's description of a joke telling contest in which every joke had to end with the same punchline: "Oh I'm sorry ma'am. I thought you said 'cohomology' " ?

Ha! That's funny! I'm almost sure that's funny! But all kidding aside, there are some great stories here, some funny, some sad, but every one of them with something to say, and not just about math. As I wrote in a review of the title story (my favorite of the collection), there is something here that gets to the heart of what it means to be human, not just what it means to be a mathematician. Because math is a part of our shared humanity, and a sorely neglected part. It's certainly more relevant than vampires and wizards are, but mathematical fiction is, I'm sad to say, doomed to get a lot less attention. The world of publishing will continue to marginalize and trivialize fiction incorporating this subject matter that is so rich, fascinating, and vitally important to all of our lives, casting it aside in favor of marketing to-- if you'll excuse a painfully overused expression--the lowest common denominator.

Math is not only one of the most essential intellectual tools we could ever hope to discover, without which our lives would be nasty, brutish and much much shorter, it is genuinely beautiful. You don't have to be a mathematician to appreciate this, any more than you need to be a musician to love music. I have often opined that through music the beauty of mathematics is made apparent even to those who do not understand it. Fiction, like music, expresses the ineffable mystery of life in a way that straightforward explanation cannot. I am a lover of beauty, be it music, mathematics, or fiction. And this beautiful collection of stories had me humming along.